Further, they're assuming causality in the direction of a decline in corporate R&D causing the rise of (generally government-supported) university research. But I don't see them providing support for that assumption.

Could it be the other way around? That government-supported research in the universities had (at least to some degree) the effect of crowding-out the corporate labs? I mean, if the government is going to foot the bill, then why would I want to spend my own money on it?